Systems and methods for susceptibility tensor imaging

ABSTRACT

The present disclosure provides a method and system for quantifying and making images of tissue anisotropy property based on magnetic resonance imaging (MRI). The systems and methods provided herein utilize orientation distribution of magnetic susceptibility to characterize magnetic susceptibility anisotropy (MSA) inside biological tissues. This MSA may be intrinsic property of the tissue or may be induced by the presence of external agents. In certain embodiments, the MSA is displayed as an orientation distribution function of susceptibility and/or may be described by mathematical quantities such as tensors (e.g., symmetric or asymmetric second order or higher order tensors) and spherical harmonics. In other embodiments, the MSA is characterized using a second order tensor named apparent susceptibility tensor (AST).

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. Provisional Patent ApplicationNo. 61/328,323 filed on Apr. 27, 2010, the entire content of which ishereby incorporated by reference.

GOVERNMENT INTEREST

The present disclosure was made with U.S. Government support under thefollowing grants: NIH/NIBIB Grant No. 4R00 EB007182-03. Accordingly, theFederal Government has rights to this invention.

TECHNICAL FIELD

The present disclosure relates to systems and methods for quantifyingand generating images of tissue anisotropy property based in magneticresonance imaging (MRI).

BACKGROUND

Magnetic resonance imaging (MRI) is a non-destructive method for theanalysis of materials and represents a new approach to medical imaging.It is generally non-invasive and does not involve ionizing radiation. Invery general terms, nuclear magnetic moments are excited at specificspin precession frequencies which are proportional to the local magneticfield. The radio-frequency signals resulting from the precession ofthese spins are received using pickup coils. By manipulating themagnetic fields, an array of signals is provided representing differentregions of the volume. These are combined to produce a volumetric imageof the nuclear spin density of the body.

MRI signals for reconstructing an image of an object are obtained byplacing the object in a magnetic field, applying magnetic gradients forslice selection, applying a magnetic excitation pulse to tilt nucleispins in the desired slice or volume, and then detecting MRI signalsemitted from the tilted nuclei spins while applying readout gradients.The detected signals may be envisioned as traversing lines in a Fouriertransformed space (k-space) with the lines aligned and spaced parallelin Cartesian trajectories or emanating from the origin of k-space inspiral trajectories.

An MRI may be used for scanning a patient's brain. The MRI may be usefulfor measuring development of the brain, particularly for scanningwhite-matter within the brain. White matter is a component of thecentral nervous system and consists of myelinated axons. Myelin acts asan insulator around nerve cells and increases the speed of transmissionof nerve signals. The multilayered myelin sheath wrapping around nerveaxons is essential for proper functioning of the central nervous system.Abnormal myelination leads to a wide range of neurological diseases anddevelopmental disorders. MRI is the preferred reference test fordiagnosing and monitoring the evolution of white-matter development andrelated diseases due to its excellent soft tissue contrast, high spatialresolution, and non-radioactive nature. However, conventional MRImethods may not provide satisfactory accuracy for quantifying themyelinated axons, and determining, for example, the amount of myelinatedaxons present in a subject's brain.

SUMMARY

According to one embodiment, a method for magnetic resonance imaging(MRI) is provided. The method includes using an MRI system to acquireimaging data of an object. The imaging data includes a plurality ofvoxels. The method includes determining orientations of the voxels. Themethod includes generating an image based on the orientations of thevoxels for depicting a characteristic of the object.

According to one embodiment, using an MRI system includes using the MRIsystem to apply a magnetic field to the object.

According to one embodiment, using an MRI system includes using the MRIsystem to acquire imaging data of the object at a plurality oforientations of the object relative to a magnetic field generated by theMRI system.

According to one embodiment, determining orientations of the voxelsincludes determining magnetic susceptibility tensors of the voxels.

According to one embodiment, determining one of vector components,eigenvalue decomposition, and invariant functions of susceptibilitytensors of the voxels, and generating an image includes generating theimage based on the one of vector components, eigenvalue decomposition,and invariant functions of the susceptibility tensors.

According to one embodiment, a method includes determining whether eachof the voxels has an eigenvalue greater than a predetermined magnitude.A method includes identifying adjacent voxels that each have aneigenvalue greater than the predetermined magnitude. For each identifiedadjacent voxel, the method includes determining whether an angle betweeneigenvectors of the identified adjacent voxels is less than apredetermined angle value. The method includes generating an image thatdepicts one or more lines extending between the identified adjacentvoxels in which the angle between eigenvectors is less than thepredetermined angle value.

According to one embodiment, a method includes generating an image basedon the magnetic susceptibility tensors for depicting a tissuecharacteristic of the object.

According to one embodiment, a method includes determining whether anangle between orientations of adjacent voxels is less than apredetermined angle value generating an image that depicts one or morelines extending between the adjacent voxels in which the angle is lessthan the predetermined angle value.

According to one embodiment, a method includes determining apparentsusceptibility tensors of the voxels.

According to one embodiment, a method includes determining adistribution function of the voxels.

According to one embodiment, the object includes a fiber structure, anda method includes identifying a set of voxels corresponding to the fiberstructure based on one of magnetic susceptibility and resonancefrequency shift of the set of voxels.

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used to limit the scope of the claimed subject matter. Further, theclaimed subject matter is not limited to implementations that solve anyor all disadvantages noted in any part of this disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing summary, as well as the following detailed description ofpreferred embodiments, is better understood when read in conjunctionwith the appended drawings. For the purposes of illustration, there isshown in the drawings exemplary embodiments; however, the presentlydisclosed subject matter is not limited to the specific methods andinstrumentalities disclosed. In the drawings:

FIG. 1 is a block diagram of a magnetic resonance imaging (MRI) systemaccording to embodiments of the present invention;

FIG. 2 is a flowchart of a method for MRI in accordance with embodimentsof the present invention;

FIGS. 3A and 3B are an illustration of in-vivo MRI images of a humanbrain in accordance with the present invention;

FIG. 4 is a top view of a representative tensor in accordance withembodiments of the present invention;

FIGS. 5A through F are an illustration of MRI images in accordance withembodiments of the present invention;

FIGS. 6A through F are an illustration of MRI images in accordance withembodiments of the present invention;

FIGS. 7A through D are an illustration of MRI images of susceptibilitiesin accordance with embodiments of the present invention;

FIGS. 8A and 8B are an illustration of brain MSA in accordance withembodiments of the present invention;

FIG. 9 is an illustration of a major susceptibility vector projectedonto an FSA map in accordance with embodiments of the present invention;

FIG. 10 is an illustration of a fiber reconstruction based on STI inaccordance with embodiments of the present invention; and

FIG. 11 is an illustration of a comparison of DTI fiber tracking and STIfiber tracking in the anterior commissure and the hippocampal commissurein accordance with embodiments of the present invention.

DETAILED DESCRIPTION

The presently disclosed subject matter now will be described more fullyhereinafter with reference to the accompanying drawings, in which some,but not all embodiments are shown. Indeed, this invention may beembodied in many different forms and should not be construed as limitedto the embodiments set forth herein; rather, these embodiments areprovided so that this disclosure will satisfy applicable legalrequirements. Like numbers refer to like elements throughout.

FIG. 1 illustrates a block diagram of a magnetic resonance imaging (MRI)system 100 according to one or more embodiments disclosed herein. Thesystem 100 may include an MRI device 110. The MRI device 110 may beconfigured for scanning and capturing an image of an object 112 such asan anatomical image of an object. The MRI system 100 may include acomputing device 114. The computing device 114 may include a processor116, a memory 118, and an object interacting application 120 that isconfigured to execute on the processor 116. The MRI system 110 mayinclude a user-interface 122, such as an image generator, that isconfigured for displaying images on a display 124 and receivinguser-input through a user-input device, such as, for example, a keyboard126.

FIG. 2 illustrates a flowchart of a method for magnetic resonanceimaging 200 in accordance with one or more embodiments of the presentinvention. The method of FIG. 2 is described as being implemented by theMRI system 100 shown in FIG. 1; however, this example method should notbe considered so limiting as the method may be applied to any suitableMRI system or other imaging system. Referring to FIG. 2, the method 200may include acquiring image data of an object 202. The image data mayinclude, for example, 3-D spatial information, gradients, and any otherdesired image data. In one or more embodiments, the image data mayinclude one or more voxels. The imaging data may be acquired using anMRI system, such as system 100, to apply a magnetic field to the object.The imaging data may be acquired at multiple data points, including, forexample, acquiring imaging data of the object at a plurality oforientations of the object relative to a magnetic field generated by theMRI system. The imaging data may also be acquired with, for example, agradient-echo or similar sequence.

The method 200 may include determining an orientation of one or morevoxels 204. For example, the one or more orientations may also be anapparent susceptibility tensor. In other embodiments, the one or moreorientations may be a magnetic susceptibility tensor. In otherembodiments, the one or more orientations may be an orientationdistribution function (ODF) of susceptibility.

The method 200 may include generating an image based on the orientationof the voxels for depicting a characteristic of the object 206. Thecharacteristic may be, for example, the presence of adjacent voxelshaving sufficiently similar orientations that may be representative of,for example, white matter within a brain of a patient.

A method may include generating an image for voxels whose majoreigen-value or FSA is above a predetermined value. For each chosenvoxel, the method may include determining the fiber orientation based onthe major eigen-vector orientation or orientation distribution function(ODF). A method may also include plotting a line between adjacentvoxels. In one or more embodiments, a line may be plotted betweenadjacent voxels if the angle between the two major eigenvectors issmaller than a predetermined value. As an example, FIG. 10 illustratesthis procedure for a region of interest (ROI) chosen from FIG. 9.

An example method may include determining one of vector components,eigenvalue decomposition, and/or invariant functions of susceptibilitytensors of each of the voxels. The method may include generating animage based on the one of the vector components, eigenvaluedecomposition, and/or invariant functions of the susceptibility tensors,or combinations thereof.

Another example method may include determining whether each of thevoxels has an eigenvalue greater than a predetermined magnitude. Amethod may also include identifying adjacent voxels that each have aneigenvalue greater than the predetermined magnitude. For each identifiedadjacent voxel, a method may include determining whether an anglebetween eigenvectors of the identified adjacent voxels is less than apredetermined angle value. For each identified adjacent voxel, a methodmay include determining whether an angle between orientations ofadjacent voxels is less than a predetermined angle value. Anotherexample method may also include generating an image that depicts one ormore lines extending between the identified adjacent voxels in which theangle between eigenvectors is less than the predetermined angle value.

Yet another example method may include generating an image based on themagnetic susceptibility tensors for depicting a tissue characteristic ofthe object. The tissue characteristic may be, for example, the presenceof white matter such as myelinated axons. A method may includeidentifying a set of voxels corresponding to the fiber structure basedon one of magnetic susceptibility and resonance frequency shift of theset of voxels

Apparent Susceptibility Tensor

One manner of determining an orientation of one or more voxels 204 mayinclude determining an apparent susceptibility tensor (AST). If it isassumed that the anisotropic susceptibility, that is the directionalsusceptibility of an object, is described by a second-order (or rank 2)tensor χ that is referred to as the apparent susceptibility tensor(AST), then the magnetic flux density vector B relative to each nucleusis related to the macroscopic flux density B₀ as:B _(i)=(δ_(ij)−σδ_(ij)−⅔χ_(ij))B _(0j)  [1]

with the further assumption that the nucleus is situated within a smallsphere of Lorentz. B_(i) is the i-th component of vector B; B_(0j) isthe j-th component of vector B₀; δ_(ij) is the Kronecker delta function;and σ is the chemical shift caused by an electronic screen effect. Thevacuum permeability μ₀ is assumed to be one for simplicity. Themacroscopic flux density B₀ is further related to the applied magneticfield vector H and the demagnetizing field h as:B _(0i)=(+δ_(ij)χ_(ij))(−H _(j) h _(j))  [2]

The demagnetizing field is a result of the loading of objects into thescanner and is generated in order to satisfy Maxwell's equations. Formodern superconductor MRI scanners, h<<H. For biological samples thatare MRI compatible, it can also be assumed that the magnitude ofsusceptibility is small such that χ_(ij)<<1. Substituting Eq. [2] intoEq. [1] and keeping only up to the first-order terms, obtains:B _(i)=(δ_(ij)−σδ_(ij)+⅓χ_(ij))(H _(j) +h _(j))  [3]

To determine the demagnetizing field, the divergence of the flux densityis zero from Maxwell's equation:∇_(i) B _(i)=0  [4]

In the absence of loading, Eq. [4] is also satisfied, which results in:∇_(i) H _(i)=0  [5]

Combining Eqs. [3], [4] and [5] while keeping terms only up to the firstorder, obtains:H _(j)∇_(i)χ_(ij)+∇_(i) h _(i)=0  [6]

To facilitate calculation, a scalar magnetic potential Φ is defined suchthat:h=−∇Φ  [7]

Substituting Eq. [7] to Eq. [6], obtains:∇² Φ=H _(ji)

  [8]

Eq. [8] may be solved in the spatial frequency domain. The solutionexpressed in the forms of Fourier transform becomes:

$\begin{matrix}{\Phi = {{FT}^{- 1}\left\{ {i\frac{k_{i}H_{j}}{2\pi\; k^{2}}{FT}\left\{ \chi_{ij} \right\}} \right\}}} & \lbrack 9\rbrack\end{matrix}$

Here, k_(i) is the i-th axis in the frequency domain and k²=k₁ ²+k₂ ²+k₃². FT and FT¹ represent the forward and inverse Fourier transformoperators respectively. Substituting Eq. [9] into Eq. [7], obtains theformula for demagnetizing field flux density as:

$\begin{matrix}{h_{i} = {{- {FT}^{- 1}}\left\{ {k_{i}\frac{k_{i^{\prime}}H_{j^{\prime}}}{k^{2}}{FT}\left\{ \chi_{i^{\prime}j^{\prime}} \right\}} \right\}}} & \lbrack 10\rbrack\end{matrix}$

MR Observable Field

The magnetic flux density seen by the nucleus may be found bysubstituting Eq. [10] into Eq. [3]. By keeping terms up to the firstorder, it may be simplified to:

$\begin{matrix}{B_{i} = {{\left( {1 - \sigma} \right)H_{i}} + {{FT}^{- 1}\left\{ {{\frac{1}{3}H_{j}{FT}\left\{ \chi_{ij} \right\}} - {k_{i}\frac{k_{i^{\prime}}H_{j^{\prime}}}{k^{2}}{FT}\left\{ \chi_{i^{\prime}j^{\prime}} \right\}}} \right\}}}} & \lbrack 11\rbrack\end{matrix}$

If the reference is set to be (1−σ)H_(i), then the off-resonance field bmay be expressed as:

$\begin{matrix}{b_{i} = {{FT}^{- 1}\left\{ {{\frac{1}{3}H_{j}{FT}\left\{ \chi_{ij} \right\}} - {k_{i}\frac{k_{i^{\prime}}H_{j^{\prime}}}{k^{2}}{FT}\left\{ \chi_{i^{\prime}j^{\prime}} \right\}}} \right\}}} & \lbrack 12\rbrack\end{matrix}$

In MRI, what is observed is signal phase instead of the full vector b.The observable phase in the subject frame of reference may be expressedas:

$\begin{matrix}{\theta = {{\gamma\;{tb}_{i}{\hat{H}}_{i}} = {{FT}^{- 1}\left\{ {{\frac{1}{3}{\hat{H}}_{i}{\hat{H}}_{j}{FT}\left\{ \chi_{ij} \right\}} - {k_{i}{\hat{H}}_{i}\frac{k_{i^{\prime}}{\hat{H}}_{j^{\prime}}}{k^{2}}{FT}\left\{ \chi_{i^{\prime}j^{\prime}} \right\}}} \right\}\gamma\; H_{0}t}}} & \left\lbrack {13.a} \right\rbrack\end{matrix}$

In the laboratory frame of reference, this is expressed as:

$\begin{matrix}{\theta = {{\gamma\;{tb}_{3}{\hat{H}}_{3}} = {{FT}^{- 1}\left\{ {{\frac{1}{3}{FT}\left\{ \chi_{33} \right\}} - {\frac{k_{3}k_{i^{\prime}}}{k^{2}}{FT}\left\{ \chi_{i^{\prime}3} \right\}}} \right\}\gamma\; H_{0}t}}} & \left\lbrack {13.b} \right\rbrack\end{matrix}$

Here, H₀ is the magnitude of the applied magnetic field; Ĥ_(i) is theunit vector along the i-th axis; and t is the time of echo (TE) in agradient echo sequence. If a sufficient number of independentmeasurements are available, Eq. [13] may be inverted to determine χ.Either frame of reference may be used in calculating the magneticsusceptibility tensor.

Determination of AST

AST may be determined by several methods or techniques as disclosedherein. In one example method, AST may be measured by rotating thesubject inside the magnet and by acquiring an image at each orientation.In another method, AST may be measured by rotating the main magneticfield if permitted. In another method, AST may be measured by acquiringa spectrum of dipole coupling and through nonlinear estimation. As anexample, the method of rotating the subject inside the magnet andacquiring an image at each orientation is demonstrated for its relativeconvenience.

Assuming that AST is a symmetric tensor, then there are six independentvariables to be determined for each tensor. In principle, sixindependent measurements are necessary that may be acquired withdifferent relative orientations between the object and main magneticfield. Additional symmetry may be imposed, for example, by assumingλ₂=λ₃. Independent measurements may be obtained by rotating the imagingobject with respect to the main magnetic field. Given a set ofmeasurements, an AST may be estimated by inverting the system of linearequations formed by Eq. [13.a] in the subject frame of reference or Eq.[13.b] in the laboratory-frame of reference. When solving Eq. [13],regularization terms may be added and iterative steps may be applied,for example, to improve accuracy and reduce artifacts.

Subject-Frame of Reference

For a subject-frame approach, images at different orientations will befirst co-registered to a chosen reference orientation. The sixrigid-body transformation parameters may be estimated using onlymagnitude images. The estimated transformation matrix may be used toregister and re-slice the real and imaginary part separately. Phase mapsmay be computed from the registered real and imaginary parts. Once allphase maps are computed and preprocessed, AST may be computed for eachvoxel. Specifically, by taking Fourier transform of both sides of Eq.[13.a], Eq. [13.a] is rewritten as:

$\begin{matrix}{{{FT}\left\{ \overset{\sim}{\theta} \right\}} = {\left( {{\frac{1}{3}{\hat{H}}_{i^{\prime}}{\hat{H}}_{j^{\prime}}} - {k_{i}{\hat{H}}_{i}\frac{k_{i^{\prime}}{\hat{H}}_{j^{\prime}}}{k^{2}}}} \right){FT}\left\{ \chi_{i^{\prime}j^{\prime}} \right\}}} & \lbrack 14\rbrack\end{matrix}$

Here, {tilde over (θ)} is the normalized phase according to:

$\begin{matrix}{\overset{\sim}{\theta} = \frac{\theta}{\gamma\; H_{0}t}} & \lbrack 15\rbrack\end{matrix}$

Given a set of n measurements, a measurement vector {tilde over (θ)}, avector of unknowns x and a system matrix A may be defined in thefrequency domain:

$\begin{matrix}{\overset{\sim}{\theta} = \begin{bmatrix}{{\overset{\sim}{\theta}}_{1}(k)} & {{\overset{\sim}{\theta}}_{2}(k)} & \ldots & {{\overset{\sim}{\theta}}_{n}(k)}\end{bmatrix}^{T}} & \lbrack 16\rbrack \\{x = \begin{bmatrix}{\chi_{11}(k)} & {\chi_{12}(k)} & {\chi_{13}(k)} & {\chi_{22}(k)} & {\chi_{23}(k)} & {\chi_{33}(k)}\end{bmatrix}^{T}} & \lbrack 17\rbrack \\{A = {\quad\begin{bmatrix}{{\frac{1}{3}{\overset{\Cap}{H}}_{1}^{(1)}{\overset{\Cap}{H}}_{1}^{(1)}} -} & {{\frac{2}{3}{\overset{\Cap}{H}}_{1}^{(1)}{\overset{\Cap}{H}}_{2}^{(1)}} -} & \ldots & {{\frac{1}{3}{\overset{\Cap}{H}}_{3}^{(1)}{\overset{\Cap}{H}}_{3}^{(1)}} -} \\{k_{i}{\overset{\Cap}{H}}_{i}^{(1)}\frac{k_{1}{\overset{\Cap}{H}}_{1}^{(1)}}{k^{2}}} & {k_{i}{\overset{\Cap}{H}}_{i}^{(1)}\frac{{k_{1}{\overset{\Cap}{H}}_{2}^{(1)}} + {k_{2}{\overset{\Cap}{H}}_{1}^{(1)}}}{k^{2}}} & \; & {k_{i}{\overset{\Cap}{H}}_{i}^{(1)}\frac{k_{3}{\overset{\Cap}{H}}_{3}^{(1)}}{k^{2}}} \\{{\frac{1}{3}{\overset{\Cap}{H}}_{1}^{(2)}{\overset{\Cap}{H}}_{1}^{(2)}} -} & {{\frac{2}{3}{\overset{\Cap}{H}}_{1}^{(2)}{\overset{\Cap}{H}}_{2}^{(2)}} -} & \ldots & {{\frac{1}{3}{\overset{\Cap}{H}}_{3}^{(2)}{\overset{\Cap}{H}}_{3}^{(2)}} -} \\{k_{i}{\overset{\Cap}{H}}_{i}^{(2)}\frac{k_{1}{\overset{\Cap}{H}}_{1}^{(2)}}{k^{2}}} & {k_{i}{\overset{\Cap}{H}}_{i}^{(2)}\frac{{k_{1}{\overset{\Cap}{H}}_{2}^{(2)}} + {k_{2}{\overset{\Cap}{H}}_{1}^{(2)}}}{k^{2}}} & \; & {k_{i}{\overset{\Cap}{H}}_{i}^{(2)}\frac{k_{3}{\overset{\Cap}{H}}_{3}^{(2)}}{k^{2}}} \\\vdots & \vdots & \vdots & \vdots \\{{\frac{1}{3}{\overset{\Cap}{H}}_{1}^{(n)}{\overset{\Cap}{H}}_{1}^{(n)}} -} & {{\frac{2}{3}{\overset{\Cap}{H}}_{1}^{(n)}{\overset{\Cap}{H}}_{2}^{(n)}} -} & \ldots & {{\frac{1}{3}{\overset{\Cap}{H}}_{3}^{(n)}{\overset{\Cap}{H}}_{3}^{(n)}} -} \\{k_{i}{\overset{\Cap}{H}}_{i}^{(n)}\frac{k_{1}{\overset{\Cap}{H}}_{1}^{(n)}}{k^{2}}} & {k_{i}{\overset{\Cap}{H}}_{i}^{(n)}\frac{{k_{1}{\overset{\Cap}{H}}_{2}^{(n)}} + {k_{2}{\overset{\Cap}{H}}_{1}^{(n)}}}{k^{2}}} & \; & {k_{i}{\overset{\Cap}{H}}_{i}^{(n)}\frac{k_{3}{\overset{\Cap}{H}}_{3}^{(n)}}{k^{2}}}\end{bmatrix}}} & \lbrack 18\rbrack\end{matrix}$

The resultant system of linear equations may be solved for each voxelusing least-squares estimation as:x=(A ^(T) A)θ⁻¹ A ^(T) ^(˜)   [19]

Once x is computed for each voxel, the entries of AST may be computedthrough a 3D inverse Fourier transform.

Laboratory-Frame of Reference

For a laboratory-frame based approach, an apparent magneticsusceptibility (AMS) may be computed for each orientation. The computedAMS map can then be registered to the reference orientation using thesame transformation parameters obtained via magnitude imageregistration. The AMS (χ₃₃′) of a given voxel on the spatiallyregistered AMS map may be expressed in terms of the underlying true AST(χ) as:χ_(33 ′) =

R  [20]

Here, R is the 3D rotation matrix that transforms an image volume tomatch a reference. The rotation matrix may be decomposed into threebasic rotation matrixes as:R=R _(x) R _(y) R _(z)  [21]

The three basic rotation matrix are given by:

$\begin{matrix}{{R_{x}(\alpha)} = \begin{bmatrix}1 & 0 & 0 \\0 & {\cos\;\alpha} & {\sin\;\alpha} \\0 & {{- \sin}\;\alpha} & {\cos\;\alpha}\end{bmatrix}} & \lbrack 22\rbrack \\{{R_{y}(\beta)} = \begin{bmatrix}{\cos\;\beta} & 0 & {{- \sin}\;\beta} \\0 & 1 & 0 \\{\sin\;\beta} & 0 & {\cos\;\beta}\end{bmatrix}} & \lbrack 23\rbrack \\{{R_{z}(\gamma)} = \begin{bmatrix}{\cos\;\gamma} & {\sin\;\gamma} & 0 \\{{- \sin}\;\gamma} & {\cos\;\gamma} & 0 \\0 & 0 & 1\end{bmatrix}} & \lbrack 24\rbrack\end{matrix}$

There is one rotation matrix R for each imaging volume. Once all AMSmaps are registered, the underlying AST can then be estimated byinverting the resultant system of linear equation for each voxel. Morespecifically, b is defined as a vector of AMS measured at n differentorientation, a vector unknown x and a system matrix B:

$\begin{matrix}{b = \begin{bmatrix}\chi_{33}^{\prime{(1)}} & \chi_{33}^{\prime{(2)}} & \ldots & \chi_{33}^{\prime{(n)}}\end{bmatrix}^{T}} & \lbrack 25\rbrack \\{x = \begin{bmatrix}{x_{11}(r)} & {x_{12}(r)} & {x_{13}(r)} & {x_{22}(r)} & {x_{23}(r)} & {x_{33}(r)}\end{bmatrix}^{T}} & \lbrack 26\rbrack \\{B = \begin{bmatrix}{R_{13}^{(1)}R_{13}^{(1)}} & {2R_{13}^{(1)}R_{23}^{(1)}} & \ldots & {R_{33}^{(1)}R_{33}^{(1)}} \\{R_{13}^{(2)}R_{13}^{(2)}} & {2R_{13}^{(2)}R_{23}^{(2)}} & \ldots & {R_{33}^{(2)}R_{33}^{(2)}} \\\vdots & \vdots & \vdots & \vdots \\{R_{13}^{(n)}R_{13}^{(n)}} & {R_{13}^{(n)}R_{23}^{(n)}} & \ldots & {R_{33}^{(n)}R_{33}^{(n)}}\end{bmatrix}} & \lbrack 27\rbrack\end{matrix}$

Here, the number in the parentheses of the upper index enumerates thenumber of orientations sampled. The difference between Eq. [26] and Eq.[17] is that Eq. [26] is expressed in the image domain while Eq. [17] isexpressed in the frequency domain. Once the three notations are defined,the AST in the image domain may be found for each voxel as:x=(B ^(T) B)⁻¹ B ^(T) b  [28]

Setting Baseline Reference

An uncertainty in phase images may be induced by, for example, receiverphase and the choice of reference frequency. In addition, subtle phasecontrast may be disguised or overwhelmed by the presence of large localsusceptibility such as bone and air. For images acquired withmultiple-channel receiver coil, a complex-valued image may bereconstructed for each channel of the coil. A low-resolution phase mapmay be extracted from each coil by low-pass filtering the phase map witha Fermi filter or by fitting with a smooth polynomial or spline-typefunction or by Laplace filtering. This low-resolution phase is thensubtracted from each coil. After removing global phases, images from allcoils are combined in complex numbers to form the final image. To ensurethat all images have a common reference, a uniform reference marker maybe inserted in the coil, imaged at each session and served as areference. Alternatively, an internal reference location can also bechosen as a reference such as the cerebral spinal fluid (CSF). Given areference point, phase at other locations may be either positive ornegative. FIGS. 3A and 3B show the intensity-reversed phase sensitiveimages (RPSI) created by weighing the magnitude image by the negativeand positive phase respectively. Here, negative phase tends to highlightvessels due to flow and the presence of iron whereas positive phasehighlights the minute structure within white matter.

Setting the reference consistently addresses several important issues inquantifying AST such as a baseline shift that affects the meansusceptibility and a potential change of anisotropy caused by thebaseline inconsistency in AMS or in the phase maps. The first effect isless significant as a constant shift in all AMS results in an additionof an identity matrix to the original AST and therefore does not affectthe anisotropy:

(+IδR)

χ

δ  [29]

The internal reference chosen may contain anisotropic susceptibility,although it is expected to be small inside CSF. If the reference regionof interest (ROI) indeed has intrinsic magnetic susceptibilityanisotropy (“MSA”), then the AST of the reference ROI will be subtractedfrom all voxels and therefore not affect the overall MSA contrast of thewhole image volume.

Solving Eq. [14] is complicated when the image phase is wrapped around2π. Phase wrapping appears commonly in high field imaging especiallywhen large off-resonance is present and when TE is relatively large. Theuncertainty in wrapped phase, if uncorrected, results in large errors inthe estimated AST. A common approach in calculating susceptibility fromphase images is to perform a phase unwrapping procedure prior to thematrix inversion. There are a number of algorithms existing in theliterature for phase unwrapping. However, performing phase unwrappingfor the calculation of AST is, unfortunately, not a feasible solutionbecause of the uncertainty in the baseline phase. When performing phaseunwrapping, a region has to be chosen as the reference. When differentreferences are chosen, the unwrapped phase may be offset by multiples of2π. It is improbable to assure that the unwrapped phases are consistentamong different orientations even if the same reference region is used,because phase changes when the object orients differently with respectto the main magnetic field.

An example solution to this problem, according to at least oneembodiment of the invention, may involve several steps describedhereinafter. In an example step, the Laplacian of the phase is computedusing only cosine and sine functions of the phase which is, thus,indifferent to the phase wrapping issue. In another example step, oncethe Laplacian is computed, the Fourier transform of the phase iscomputed through the Fourier transform of the Laplacian. In anotherexample step, a phase map is multiplied by a mask, such as 1 inside thebrain and zero outside, and the Laplacian operator is applied for asecond time. This process may be iterated. Specifically, the Laplacianof the phase image is computed using the following trigonometricrelationship:∇²θ=cos θ²

nθs

θ ²

sθ  [30]

Furthermore, the Laplacian of the trigonometric functions may becomputed via Fourier transform as:∇² s

θ=(2π)² FT ⁻¹ {k ² FT{sin θ}}  [31]∇² c

θ=(2π)² FT ⁻¹ {k ² FT{cos θ}}  [32]

Once the Laplacian is computed, the Fourier transform of the phase image(the left side of Eq. [14]) can then be computed as:

$\begin{matrix}{{{FT}\left\{ \theta \right\}} = {{- \frac{1}{4\pi^{2}}}\frac{1}{k^{2}}{FT}\left\{ {\nabla^{2}\theta} \right\}}} & \lbrack 33\rbrack\end{matrix}$

In the numerical implementation of this approach, a small number(1.0×10⁻⁹) is added to k² in the denominator to avoid dividing by zero.In addition, the Laplacians are computed on a matrix that is twice thesize of the original image. In expanding the size of the matrix, theoriginal phase image is mirrored to different quadrants, creating aneven function, which, therefore, guarantees the computed Laplacian to bereal. A further advantage of this method is that the background phase isautomatically removed once the Laplacian is operated on masked phasemaps. The mask may be generated based on the magnitude image whichdefines the interior of the brain (or region of interest) and exterior.

Quantifying MSA

The computed AST is coordinate system dependent. To define rotationalinvariant quantities, eigen-value decomposition of the AST is performedand three principal susceptibilities are defined. The three principalsusceptibilities are denoted as χ₁, χ₂, and χ₃, ranked in a descendingorder. There is also an eigen-vector corresponding to each principalsusceptibility. The major eigen-vector points towards the direction thatexhibits the largest magnetic susceptibility. Fractional susceptibilityanisotropy (FSA) is defined to quantitatively characterize anisotropyobserved in susceptibility as:

$\begin{matrix}{{FSA} = \sqrt{\frac{3\left( {\left( {\chi_{1} - \overset{\_}{\chi}} \right)^{2} + \left( {\chi_{2} - \overset{\_}{\chi}} \right)^{2} + \left( {\chi_{3} - \overset{\_}{\chi}} \right)^{2}} \right)}{2\left( {\chi_{1}^{2} + \chi_{2}^{2} + \chi_{3}^{2}} \right)}}} & \left\lbrack {34.a} \right\rbrack\end{matrix}$

where χ is the mean susceptibility. Eigen-decomposition also providesthree eigen-vectors that define the orientation of the three principalsusceptibilities.

Alternatively, MSA may be defined as:

$\begin{matrix}{{MSA} = {\chi_{1}\frac{\chi_{2} + \chi_{3}}{2}}} & \left\lbrack {34.b} \right\rbrack\end{matrix}$

An example advantage of this definition is that it is indifferent to thereference frequency.

The shape of the tensor may be visualized by a susceptibility ellipsoidwhose radii are defined by the principal susceptibilities. Whenprincipal susceptibilities are negative, their absolute values may beused instead or a baseline may be added. An example susceptibilityellipsoid is shown in FIG. 4. The shape of the tensor may becharacterized by a shape parameter T defined as:

$\begin{matrix}{T = \frac{{\ln\left( {x_{2}/x_{3}} \right)} - {\ln\left( {x_{1}/x_{2}} \right)}}{{\ln\left( {x_{2}/x_{3}} \right)} + {\ln\left( {x_{1}/x_{2}} \right)}}} & \lbrack 35\rbrack\end{matrix}$

Other scalar parameters can also be defined based on the threeeigen-values.

Experimental Demonstration

Experimental Setup

In accordance with an experiment of the disclosed subject matter, todemonstrate the existence of MSA and to illustrate the proposedsusceptibility tensor imaging (STI) technique, ex vivo MR microscopy wasperformed on mouse brains at a small-bore 7T MRI scanner.

According to the procedure, animals (adult (9-12 weeks) C57BL/6 mice[The Jackson Laboratory, Bar Harbor, Me.; Charles River, Raleigh, N.C.])are anesthetized with Nembutal. A catheter is inserted into the leftventricle of the mouse heart. The animal is perfused with a peristalticpump first with a mixture of 0.9% saline and ProHance (10:1, v:v)(Bracco Diagnostics, Princeton, N.J.), then with a mixture of 10%buffered formalin and ProHance (10:1, v:v). The perfused mouse brain iskept within the skull to prevent any potential damage to the braincaused by surgical removal. This fixation procedure simultaneouslypreserves the tissue and preferentially enhances the signal by reducingthe spin lattice relaxation time. In addition, in comparison toconventional fixation techniques, the active staining technique appearsto largely preserve the diffusion property of the brain tissues. Forexample, a mean diffusivity of 0.5×10⁻³ mm²/s has been measured for graymatter and 0.4×10⁻³ mm²/s for white matter.

Ultra-high resolution 3D SPGR images were acquired using a 7T horizontalbore magnet with shielded coil providing gradients of 160 G/cm. Theimaging parameters were: matrix=256×256×256, FOV=22×22×22 mm³, TE=8 ms,and TR=100 ms. All images were acquired using a 7T magnet with shieldedcoil providing gradients of 770 mT/m over 90 mm FOV. The system iscontrolled by a GE EXCITE MR imaging console. The specimen was sealedtightly inside a cylindrical tube (length 30 mm and diameter 11 mm). Toallow free rotation, the tube was contained within and taped to a hollowsphere (diameter 30 mm). The sphere containing the specimen was placedinside a dual-channel mouse coil (diameter 31 mm, M2M imaging Corp,Cleveland Ohio). After each acquisition, the sphere was rotated to adifferent orientation and the acquisition was repeated. A total of 19orientations were sampled that roughly cover the spherical surfaceevenly. To avoid-introduced frequency shifts, the same shimming currentswere applied for all directions. The carrier frequency was also kept thesame. Temperature was monitored through the scans and fluctuation wasrecorded to be below 1° C.

Orientation-Dependent AMS and AST

AMS was computed for each orientation. The computed AMS maps are thencoregistered to a reference orientation. Examples of the orientationdependent AMS are shown in FIGS. 5A through F.

The AST was computed for the ex vivo mouse brain data. The threediagonal elements of the AST from a representative slice are shown inFIGS. 6A through F. The anisotropy existing in the AST is clearlyevident. The anisotropy is the strongest in white matter whilerelatively weaker in the gray matter. The observed anisotropy is not aconsequence of the tensor model. Isotropic medium may be described by adiagonal tensor with equal diagonal entries.

The AST may be further decomposed into three eigen-vectors and threeassociated eigen-values. Examples of eigen-value maps are shown in FIGS.7A through D. FSA and color-coded FSA is shown in FIGS. 7A, B, C, and D.The major eigen-vector is projected onto the plane in an example regionof interest in FIGS. 8A and 8B.

Application

MSA allows for image contrast generation for non-invasive ex vivo and invivo MRI. As one example, MSA may be acquired, analyzed, and visualizedwith STI. This contrast may be a result of intrinsic tissue property ormay be induced by external agents. This technique may be applied in anyin vivo or ex vivo MRI imaging/microscopy where the imaged subjectexhibits MSA.

Tissue Contrast

Biologic tissues such as brain white and gray matter contain variousamounts of iron and macromolecules. These iron and macromolecules carryan intrinsic magnetic susceptibility tensor that is determined by theiron property, the structural configuration of the macromolecules, andthe dipolar coupling between different nuclei. Furthermore, once theseirons and macromolecules are bonded with local tissue, the binding willenforce additional constraints on the orientation of the macromoleculesthus affecting the apparent susceptibility tensor observed within onevoxel. Consequently, because of tissue heterogeneity, there will be adifference between their AMS, AST, and MSA. Images may then be createdby using these quantities to visualize and enhance tissue contrast.These images include a display of AMS, elements of AST, eigen-values andeigen-vectors of AST, and a combination thereof such as a magnitudeimage weighted by AMS. Tissue structural changes caused by tumor,stroke, traumatic injury, and iron-content changes caused bydevelopmental iron deficiency and aging will then manifest in thechanges of those quantities.

Brain Connectivity and Tractography

Currently, diffusion tensor MRI is a non-invasive method for visualizingwhole brain white matter fiber tracts in vivo. DTI fiber tractographymay be used for in vivo mapping of brain neural networks and may be usedin the fields of diagnostic radiology, neuroscience, psychology andpsychiatry. The basic assumption of DTI fiber tractography is that themost preferable diffusion orientation of water molecules inside whitematter is along the fibers. Therefore, by following the majoreigenvector direction, one is able to trace white matter fibers in threedimensions inside the whole brain. DTI tractography has so far facedthree main challenges. Currently, it is thought that there is no otherin vivo tracking method that may be used to validate DTI tractography.DTI tractography is ineffective of resolving multiple fiber orientationswithin one voxel. Third, DTI is extremely susceptible to motion andoff-resonance artifacts. The image quality and spatial resolution of DTIas a result has so far been severely limited.

In addition, DTI has encountered significant difficulties at ultra-highfield strength (7T and above). Although ultra high field offers strongerraw signal strength, this strength has been so far difficult if notimpossible for DWI/DTI to take advantage of. Many challenges still needto be overcome before improved DWI/DTI image quality may be obtained at7T. The difficulties include: more rapid T2 and T2* decay that negatesthe gain of raw signal strength; high specific absorption rate (SAR)that limits slice coverage of the brain and causes safety concern;severe inhomogeneous B1-field that induces additional signal-to-noise(SNR) loss; and severe off-resonance artifacts that create severegeometrical distortion for echo-planner-imaging (EPI) and blurring forspiral imaging. The current DWI/DTI quality at 7T is still significantlybelow that of 3T. The development in this area has been limited toimplementing DWI/DTI at ultra-high field. Single shot EPI, themost-widely used technique for DWI acquisition, has been impractical at7T and higher, even at the typical 2×2 mm² resolution. Until moresophisticated technology is developed to address the aforementionedchallenges, routine application of DWI/DTI at 7T will remainimpractical.

More importantly, DTI primarily sensitizes to geometrical changes andoffers few insights on tissue specificity. STI may offer a number ofimportant benefits that will significantly enhance pediatricneuroimaging, such as: new insights on white matter architecturecomplimenting and potentially cross-validating DTI results, superiorresolution (0.4×0.4×1.0 mm³), safer and significantly smaller specificabsorption rate (SAR), inherent advantage at high and ultra-high fieldswhere susceptibility effect is amplified, compatibility with ultra-shortT2 species and specific information on tissue composition of iron andproteins that are important for brain development.

The orientation information offered by STI may be used to reconstructwhite matter fiber pathways, thus providing a much-needed second in vivomethod for mapping brain white matter fiber pathways.

Susceptibility Tensor Spectroscopic Imaging (STSI)

Within an image volume, each voxel contains an ensemble of microscopicsusceptibility tensors. The measured AST is an ensemble average of allmicroscopic susceptibility tensors. Each microscopic tensor is anintrinsic property of the molecules within the voxel. In a solutionform, the orientation information of the microscopic tensor is averagedout if molecules are orienting randomly or are tumbling quickly.However, in an ordered structure such as brain tissue and especially thewhite matter, the rotational mobility of those molecules is restricted.Consequently, there will be some residual orientation information withineach voxel. The signal observed in a typical proton MRI experiment isprimarily from water molecules due to their relatively long T2 and T2*values compared to those of macromolecules. Both free water protons andprotons exchanged from macromolecules are included. Diffusion of watermolecules within brain tissue, especially within white matter, isanisotropic. Therefore, this anisotropic diffusion process cannotaverage out the surrounding anisotropic susceptibility tensor. As aresult, the residual orientation information will manifest as afrequency spectrum that may be obtained in a spectroscopic imagingexperiment. The frequency range of this residual dipole field istypically within 0.1 ppm, much smaller than that of NAA (2 ppm) forexample. The spectrum distribution may be expressed as:

$\begin{matrix}{\omega = {\gamma\; B_{0}{\int_{\theta}{\int_{\varphi}{{p\left( {\theta,\varphi} \right)}{R_{\chi}^{T}\left( {\theta,\varphi} \right)}{R\left( {\theta,\varphi} \right)}\ {\mathbb{d}\theta}\ {\mathbb{d}\varphi}}}}}} & \lbrack 36\rbrack\end{matrix}$Here, p(θ,φ) is the ODF of the molecular orientation; χ is the molecularsusceptibility tensor expressed in the molecular coordinate; and R isthe rotation matrix between the laboratory frame and the molecularframe. Once the spectrum is obtained, the preferable orientation of themolecules may be estimated.

Alternatively, susceptibility tensor spectroscopic imaging (STSI) canalso be conducted on other nuclei that exhibit NMR signals. For example,direct STSI of 13C, 15N, 31P and 19F would provide a more directexamination of the molecular susceptibility tensor. Such examinationwould not depend on the diffusion interaction between water protons andthe microscopic susceptibility tensor. The signal gain of hyperpolarizednuclei such hyperpolarized 13C will aid the detection the MSA greatly.

Molecular Imaging

Molecular imaging is another important area of application for themethodology developed here and the interaction mechanism described bythis invention between water proton diffusion and microscopicsusceptibility. The method may be used to guide the design of molecularcontrast agent and may be used to detect small concentrations of theseagents once injected into the tissue. Specific exogenous contrast agentsmay be designed to enhance its MSA by manipulating its structure and byadding frequency-shifting atoms. These contrast molecules may bedesigned to allow certain preferable binding configurations andorientations with tissue macromolecules thus to further enhance localMSA. This invention provides the methodology to further detect andenhance the tissue-specific and pathology-specific anisotropic shifteffect. Imaging of this class of molecular contrast agent will not justsimply rely on T1 or T2* effects. Rather, it will rely on theanisotropic magnetic field generated by these agents.

In accordance with embodiments of the present invention, an MRI systemas disclosed herein may be implemented on any computing device suitablefor implementing a transaction.

As will be appreciated by one skilled in the art, aspects of the presentinvention may be embodied as a system, method or computer programproduct. Accordingly, aspects of the present invention may take the formof an entirely hardware embodiment, an entirely software embodiment(including firmware, resident software, micro-code, etc.) or anembodiment combining software and hardware aspects that may allgenerally be referred to herein as a “circuit,” “module” or “system.”Furthermore, aspects of the present invention may take the form of acomputer program product embodied in one or more computer readablemedium(s) having computer readable program code embodied thereon.

Any combination of one or more computer readable medium(s) may beutilized. The computer readable medium may be a computer readable signalmedium or a computer readable storage medium (including, but not limitedto, non-transitory computer readable storage media). A computer readablestorage medium may be, for example, but not limited to, an electronic,magnetic, optical, electromagnetic, infrared, or semiconductor system,apparatus, or device, or any suitable combination of the foregoing. Morespecific examples (a non-exhaustive list) of the computer readablestorage medium would include the following: an electrical connectionhaving one or more wires, a portable computer diskette, a hard disk, arandom access memory (RAM), a read-only memory (ROM), an erasableprogrammable read-only memory (EPROM or Flash memory), an optical fiber,a portable compact disc read-only memory (CD-ROM), an optical storagedevice, a magnetic storage device, or any suitable combination of theforegoing. In the context of this document, a computer readable storagemedium may be any tangible medium that can contain, or store a programfor use by or in connection with an instruction execution system,apparatus, or device.

A computer readable signal medium may include a propagated data signalwith computer readable program code embodied therein, for example, inbaseband or as part of a carrier wave. Such a propagated signal may takeany of a variety of forms, including, but not limited to,electro-magnetic, optical, or any suitable combination thereof. Acomputer readable signal medium may be any computer readable medium thatis not a computer readable storage medium and that can communicate,propagate, or transport a program for use by or in connection with aninstruction execution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, RF, etc., or any suitable combination ofthe foregoing.

Computer program code for carrying out operations for aspects of thepresent invention may be written in any combination of one or moreprogramming languages, including an object oriented programming languagesuch as Java, Smalltalk, C++ or the like and conventional proceduralprogramming languages, such as the “C” programming language or similarprogramming languages. The program code may execute entirely on theuser's computer, partly on the user's computer, as a stand-alonesoftware package, partly on the user's computer and partly on a remotecomputer or entirely on the remote computer or server. In the lattersituation scenario, the remote computer may be connected to the user'scomputer through any type of network, including a local area network(LAN) or a wide area network (WAN), or the connection may be made to anexternal computer (for example, through the Internet using an InternetService Provider).

Aspects of the present invention are described below with reference toflowchart illustrations and/or diagrams of methods, apparatus (systems)and computer program products according to embodiments of the invention.For example, aspects of the present invention are described withreference to the diagram of FIG. 1 and the flowchart of FIG. 2. It willbe understood that each block of the flowchart illustrations and/ordiagrams, and combinations of blocks in the flowchart illustrationsand/or diagrams, can be implemented by computer program instructions.These computer program instructions may be provided to a processor of ageneral purpose computer, special purpose computer, or otherprogrammable data processing apparatus to produce a machine, such thatthe instructions, which execute via the processor of the computer orother programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/ordiagram block or blocks.

These computer program instructions may also be stored in a computerreadable medium that can direct a computer, other programmable dataprocessing apparatus, or other devices to function in a particularmanner, such that the instructions stored in the computer readablemedium produce an article of manufacture including instructions whichimplement the function/act specified in the flowchart and/or blockdiagram block or blocks.

The computer program instructions may also be loaded onto a computer,other programmable data processing apparatus, or other devices to causea series of operational steps to be performed on the computer, otherprogrammable apparatus or other devices to produce a computerimplemented process such that the instructions which execute on thecomputer or other programmable apparatus provide processes forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof code, which comprises one or more executable instructions forimplementing the specified logical function(s). It should also be noted,in some alternative implementations, the functions noted in the blockmay occur out of the order noted in the figures. For example, two blocksshown in succession may, in fact, be executed substantiallyconcurrently, or the blocks may sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each block of the block diagrams and/or flowchart illustration, andcombinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a,” “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed. Thedescription of the present invention has been presented for purposes ofillustration and description, but is not intended to be exhaustive orlimited to the invention in the form disclosed. Many modifications andvariations will be apparent to those of ordinary skill in the artwithout departing from the scope and spirit of the invention. Theembodiment was chosen and described in order to best explain theprinciples of the invention and the practical application, and to enableothers of ordinary skill in the art to understand the invention forvarious embodiments with various modifications as are suited to theparticular use contemplated.

What is claimed is:
 1. A method for magnetic resonance imaging (MRI)comprising: using an MRI system to acquire susceptibility tensor data ofan object, the susceptibility tensor data being rank 2 or higher andincluding a plurality of voxels; determining orientations of the voxels;determining whether each of the voxels has an eigenvalue greater than apredetermined magnitude; identifying adjacent voxels that each have aneigenvalue greater than the predetermined magnitude; for each identifiedadjacent voxel, determining whether an angle between eigenvectors of theidentified adjacent voxels is less than a predetermined angle value; andgenerating an image based on the orientations of the voxels fordepicting a characteristic of the object, wherein generating an imagecomprises generating an image that depicts one or more lines extendingbetween the identified adjacent voxels in which the angle betweeneigenvectors is less than the predetermined angle value.
 2. The methodof claim 1, wherein using an MRI system comprises using the MRI systemto apply a magnetic field to the object.
 3. The method of claim 1,wherein using an MRI system comprises using the MRI system to acquiresusceptibility tensor data of the object at a plurality of orientationsof the object relative to a magnetic field generated by the MRI system.4. The method of claim 1, comprising determining one of vectorcomponents, eigenvalue decomposition, and invariant functions ofsusceptibility tensors of the voxels, and wherein generating an imagecomprises generating the image based on the one of vector components,eigenvalue decomposition, and invariant functions of the susceptibilitytensors.
 5. The method of claim 1, wherein generating an image comprisesgenerating the image based on the susceptibility tensors for depicting atissue characteristic of the object.
 6. The method of claim 1, whereindetermining orientations of the voxels comprises determining apparentsusceptibility tensors of the voxels.
 7. The method of claim 1, whereindetermining orientations of the voxels comprises determining anorientation distribution function of the voxels, the orientationdistribution function being susceptibility as a function of magneticfield or object orientation.
 8. The method of claim 1, wherein theobject includes a fiber structure, and wherein the method comprisesidentifying a set of voxels corresponding to the fiber structure basedon one of magnetic susceptibility tensors and resonance frequency shiftof the set of voxels.
 9. A magnetic resonance imaging (MRI) system,comprising: an MRI device configured to acquire susceptibility tensordata of an object, the susceptibility tensor data being rank 2 or higherand including a plurality of voxels; and an image generator configuredto: determine orientations of the voxels; determine whether each of thevoxels has an eigenvalue greater than a predetermined magnitude;identify adjacent voxels that each have an eigenvalue greater than thepredetermined magnitude; for each identified adjacent voxel, determinewhether an angle between eigenvectors of the identified adjacent voxelsis less than a predetermined angle value; control a display to generatean image based on the orientations of the voxels for depicting acharacteristic of the object; and control the display to generate animage that depicts one or more lines extending between the identifiedadjacent voxels in which the angle between eigenvectors is less than thepredetermined angle value.
 10. The system of claim 9, wherein the MRIdevice is configured to acquire susceptibility tensor data of the objectat a plurality of orientations of the object relative to a magneticfield generated by the MRI system.
 11. The system of claim 9, whereinthe image generator is configured to: determine one of vectorcomponents, eigenvalue decomposition, and invariant functions ofsusceptibility tensors of the voxels; and control the display togenerate an image based on the one of vector components, eigenvaluedecomposition, and invariant functions of the susceptibility tensors.12. The system of claim 9, wherein the image generator is configured tocontrol the display to generate an image based on the susceptibilitytensors for depicting a tissue characteristic of the object.
 13. Thesystem of claim 9, wherein the image generator is configured todetermine one of a magnetic susceptibility tensor and an apparentsusceptibility tensor of the voxels.
 14. The system of claim 9, whereinthe image generator is configured to determine an orientationdistribution function of the voxels.
 15. The system of claim 9, whereinthe object includes a fiber structure, and wherein the image generatoris configured to identify a set of voxels corresponding to the fiberstructure based on one of magnetic susceptibility tensor and resonancefrequency shift of the set of voxels.
 16. A computer program product forcontrolling a magnetic resonance imaging (MRI) system, said computerprogram product comprising: a non-transitory computer readable storagemedium having computer readable program code embodied therewith, thecomputer readable program code comprising: computer readable programcode configured to use an MRI device to acquire susceptibility tensordata of an object, the susceptibility tensor data being rank 2 or higherand including a plurality of voxels; computer readable program codeconfigured to determine orientations of the voxels; computer readableprogram code configured to determine whether each of the voxels has aneigenvalue greater than a predetermined magnitude; computer readableprogram code configured to identify adjacent voxels that each have aneigenvalue greater than the predetermined magnitude; computer readableprogram code configured to, for each identified adjacent voxel,determine whether an angle between eigenvectors of the identifiedadjacent voxels is less than a predetermined angle value; computerreadable program code configured to control a display to generate animage based on the orientations of the voxels for depicting acharacteristic of the object; and computer readable program codeconfigured to control the display to generate an image that depicts oneor more lines extending between the identified adjacent voxels in whichthe angle between eigenvectors is less than the predetermined anglevalue.
 17. A method for magnetic resonance imaging (MRI) comprising:using an MRI system to acquire susceptibility tensor data of an object,the susceptibility tensor data being rank 2 or higher and including aplurality of voxels; determining orientations of the voxels; determiningwhether an angle between orientations of adjacent voxels is less than apredetermined angle value; and generating an image based on theorientations of the voxels for depicting a characteristic of the object,wherein generating an image comprises generating an image that depictsone or more lines extending between the adjacent voxels in which theangle is less than the predetermined angle value.
 18. A magneticresonance imaging (MRI) system, comprising: an MRI device configured toacquire susceptibility tensor data of an object, the susceptibilitytensor data being rank 2 or higher and including a plurality of voxels;and an image generator configured to: determine orientations of thevoxels; determine whether an angle between orientations of adjacentvoxels is less than a predetermined angle value; control a display togenerate an image based on the orientations of the voxels for depictinga characteristic of the object; and control the display to generate animage depicting a characteristic of the object comprises generating animage that depicts one or more lines extending between the adjacentvoxels in which the angle is less than the predetermined angle value.19. A computer program product for controlling a magnetic resonanceimaging (MRI) system, said computer program product comprising: anon-transitory computer readable storage medium having computer readableprogram code embodied therewith, the computer readable program codecomprising: computer readable program code configured to acquiresusceptibility tensor data of an object, the susceptibility tensor databeing rank 2 or higher and including a plurality of voxels; computerreadable program code configured to determine orientations of thevoxels; computer readable program code configured to determine whetheran angle between orientations of adjacent voxels is less than apredetermined angle value; computer readable program code configured tocontrol a display to generate an image based on the orientations of thevoxels for depicting a characteristic of the object; and computerreadable program code configured to control the display to generate animage depicting a characteristic of the object comprises generating animage that depicts one or more lines extending between the adjacentvoxels in which the angle is less than the predetermined angle value.